A framework for predicting accuracy limitations in large-eddy simulation

The accuracy of large-eddy simulations is limited, among other things, by the quality of the subgrid parametrization and the numerical contamination of the smaller retained flow structures. We characterize the total simulation error in terms of the “subgrid-activity” s, which measures the relative turbulent dissipation rate (0⩽s⩽1) and the “subgrid resolution” r. This analysis is applied to turbulent mixing of a “Smagorinsky fluid” using a finite volume discretization of fourth order accuracy. On fixed coarse grids, i.e., at constant computational cost, the total simulation error decreases monotonically with filter width Δ for large s while for smaller s the total error may even increase with decreasing Δ. The corresponding modeling- and spatial discretization-error contributions are quantified at various resolutions.